# Binary operations

Binary operations between two objects can be handled in a variety of ways in Horace. You can either use the Matlab symbols +, - , *, / and \, or you can use the explicit function names `plus, minus, mtimes, mrdivide`

and `mldivide`

.

There are several options for the input parameters to binary operations

## Contents

# sqw objects

Let us take for our example the addition operator '+', and our initial single sqw object is called `w1`

and has the 'pix' array retained (note this is an important point - you can have an sqw object without the pix array by converting a dnd object to sqw. In that case the result is referred to as an sqw object of dnd type. In our example `w1`

has a pix array, so is referred to as an sqw of sqw type).

## Single sqw object

You can add to w1 in the following way

wout = w1 + w2_sqw wout = w1 + w2_sqw_dnd_type wout = w1 + w2_dnd wout = w1 + scalar

The conditions for these operations are as follows:

`w2_sqw`

is an sqw of sqw type, with a pix array of identical size to the pix array of`w1`

. There is only really one circumstance in which doing a binary operation of this type makes sense - when a background dataset has been created that maps exactly onto the real dataset, and needs to be subtracted.

`w2_sqw_dnd_type`

is an sqw of dnd type (i.e. no it has pix array) whose plot axes overlap exactly with those of`w1`

. An example is taking a 1d cut along the energy axis from two different regions of reciprocal space, and then adding or subtracting one from the other. In this case the output will be a sqw object of dnd type, since the pixel information has lost its connection with the signal and error that are plottable.

`w2_dnd`

as above, but`w2_dnd`

is a dnd object rather than an sqw of dnd type. Similarly to the above, the output is an sqw object of dnd type.

`scalar`

is a single number, e.g. if you want to add 4.782 to all of the data in`w1`

. The output stays as a full sqw of sqw type (with pix array).

## Array of sqw objects

You can use the same binary operation syntax as for single sqw objects, with the following conditions

`w2_sqw`

is either an array of sqw of sqw type objects with the pix array of each element matching the pix array of each element of`w1`

. Or a single sqw object if the pix array happens to be the same size for all elements of the`w1`

array.

`w2_sqw_dnd`

is as above, i.e. an array of dnd-type sqw objects whose plot axes match element by element those of the array`w1`

.

`w2_dnd`

same rules as for sqw of dnd type above.

`scalar`

the same scalar is subtracted from every pix array in the array of sqw objects.

There is one additional possibility

wout = w1 + numeric_array

`numeric_array`

is an array of scalars whose size matches the size of the sqw array. The output will continue to be an sqw of sqw type, with a pix array.

# dnd objects

Note that here we will use the phrase dnd object also to mean sqw object of dnd type, since the two are very closely related.

## Single dnd object

The choices for a dnd object are:

wout = w1 + w2_sqw wout = w1 + w2_sqw_dnd_type wout = w1 + w2_dnd wout = w1 + scalar

The forms of these objects are as described for the sqw case. In all cases the output will be a dnd object. Note that the pix field of `w2_sqw`

is ignored for this operation.

## Array of dnd objects

As with arrays of sqw objects, there is one further choice compared to a single dnd:

wout = w1 + numeric_array

As for sqw objects, the numeric array has to be the same size as the array of dnd objects.

# List of operations and their equivalent code

The arithmetic operations above correspond to equivalent Matlab functions. You should never need to use these, but for reference the corresponding functions are:

w1 + w2 --> plus(w1,w2) w1 - w2 --> minus(w1,w2) w1 * w2 --> mtimes(w1,w2) w1 / w2 --> mrdivide(w1,w2) w1 \ w2 --> mldivide(w1,w2) w1 ^ w2 --> mpower(w1,w2)

**Important** the matrix operations *, /, \ and ^ (mtimes, mrdivide, mldivide and mpower) are performed **element-by-element**. So the equivalent Matlab routines would be .*, ./, .\ and .^